The rate of change for the profit function, based on the number of books sold, is a constant $1.50 per book. This means that for each additional book sold within the given range, the profit increases by $1.50.
The rate of change for a function represents how the output (profit in this case) changes concerning the input (number of books sold). To find the rate of change, we can calculate the average rate of change between two points on the table.
Let's consider the first two points (100 books and 250 books):
Average Rate of Change (AROC) = (f(250) - f(100)) / (250 - 100)
AROC = ($275.00 - $50.00) / (250 - 100) = $225.00 / 150 = $1.50/book
Now, consider the next two points (250 books and 300 books):
AROC = ($350.00 - $275.00) / (300 - 250) = $75.00 / 50 = $1.50/book
Finally, for the last two points (300 books and 350 books):
AROC = ($425.00 - $350.00) / (350 - 300) = $75.00 / 50 = $1.50/book
The rate of change for the function is consistently $1.50 per book sold throughout the given range.
The question probable may be:
The table shows the profit from a school book fair based on the number of books sold. What is the rate of change for the function represented in the table?
$0.50
$0.67
$1.07
$1.50
Book sold Profit f(x)
(X)
100 ║ $50.00
250 ║ $275.00
300 ║ $350.00
350 ║ $425.00